Dynamic Biochemistry. Enzyme Kinetics 0-471-40120-X

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An Introduction to Computational Biochemistry. C. Stan Tsai Copyright ¶ 2002 by Wiley-Liss, Inc. ISBN: 0-471-40120-X

7 DYNAMIC BIOCHEMISTRY: ENZYME KINETICS

Enzymes are biocatalysts, as such they facilitate rates of biochemical reactions. Some of the important characteristics of enzymes are summarized. Enzyme kinetics is a detailed stepwise study of enzyme catalysis as affected by enzyme concentration, substrate concentrations, and environmental factors such as temperature, pH, and so on. Two general approaches to treat initial rate enzyme kinetics, quasi-equilibrium and steady-state, are discussed. Cleland’s nomenclature is presented. Computer search for enzyme data via the Internet and analysis of kinetic data with Leonora are described.

7.1. CHARACTERISTICS OF ENZYMES Enzymes are globular proteins whose sole function is to catalyze biochemical reactions. The most important properties of all enzymes are their catalytic power, specificity, and capacity to regulation. The characteristics of enzymes (Copeland, 2000; Fersht, 1985; Kuby, 1991; Price and Stevens, 2000) can be summarized as follows:

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All enzymes are proteins: The term enzymes refers to biological catalysts, which are proteins with molecular weights generally ranging from 1.5 ; 10 to 10 daltons. The nonprotein biocatalysts such as catalytic RNA and DNA are known as ribozymes (Doherty and Doudna, 2000; Scott and Klug, 1996) 123

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and deoxyribozymes (Li and Breaker, 1999; Sheppard et al., 2000), respectively, while engineered catalytic antibodies are called abzymes (Benkovic, 1992; Hilvert, 2000). Enzymes increase the rate but do not influence the equilibrium of biochemical reactions: Enzymes are highly efficient in their catalytic power displaying rate enhancement of 10 to 10 times those of uncatalyzed reactions without changing the equilibrium constants of the reactions. Enzymes exhibit a high degree of specificity for their substrates and reactions: Enzymes are highly specific both in the nature of the substrate(s) that they utilize and in the types of reactions that they catalyze. Enzymes may show absolute specificity by a catalyzing reaction with a single substrate. Enzymes may display chemical (bond) specificity by promoting transformation of a particular chemical functional group (e.g., hydrolysis of esteric bond by esterases or phosphorylation of primary hydroxy group of aldohexoses by hexokinase). The stereospecificity refers to the ability of enzymes to choose only one of the enantiomeric pair of a chiral substrate in chiral stereospecificity, such as -lactate dehydrogenase versus -lactate dehydrogenase. One of the most subtle stereospecificities of enzymes relates their ability to distinguish between two identical atoms/groups (proR versus proS) bonded to a carbon atom in prochiral stereospecificity (Hanson, 1966), such as proR glycerol3-phosphate dehydrogenase versus proS glycerol-3-phosphate dehydrogenase. Some enzymes require cofactors for the activities: Enzymes that require covalent cofactors (prosthetic groups, e.g., heme in cytochromes) or noncovalent cofactors (coenzymes, e.g., NAD(P)> in dehydrogenases) for activities are called haloenzymes (or simply enzymes). The protein molecule of a haloenzyme is termed proenzyme. The prosthetic group/coenzyme dictates the reaction type catalyzed by the enzyme, and the proenzyme determines the substrate specificity. The active site of an enzyme (Koshland, 1960) is the region that specifically interacts with the substrate: A number of generalizations concerning the active site of an enzyme are as follows: 1. The active site of an enzyme is the region that binds the substrates (and cofactors, if any) and contributes the catalytic residues that directly participate in the making and breaking of bonds. 2. The active site takes up a relatively small part of the total dimension of an enzyme. 3. The active site is a three-dimensional entity and dynamic. 4. Active sites are generally clefts or crevices. 5. Substrates are bound to the active site of enzymes by noncovalent bonds. 6. The specificity of binding depends on the precisely defined arrangement of atoms in an active site. 7. The induced fit model (Koshland, 1958) has been proposed to explain how the active site functions.

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Enzymatic catalysis involves formation of an intermediate enzyme—substrate complex. Enzymes lower the activation energies of reactions.

CHARACTERISTICS OF ENZYMES

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The activity of some enzymes are regulated (Hammes, 1982) as follows: 1. The enzyme concentration in cells is regulated at the synthetic level by genetic control (Gottesman, 1984), which may occur positively or negatively. 2. Some enzymes are synthesized in an inactive precursor form known as proenzymes or zymogens, which are activated at a physiologically appropriate time and place. 3. Another control mechanism is covalent modifications (Freeman and Hawkins, 1980, 1985) such as reversible phosphorylation, glycosylation, acylation, and so on. These modifications are normally reversible catalyzed by separate enzymes. 4. The enzymatic activities are also subjected to allosteric/cooperative regulations (Monad et al., 1965; Perutz, 1990; Ricard and Cornish-Bowden, 1987). A regulatory molecule (effector) binds to the regulatory site (allosteric site) distinct from the catalytic site to affect one or more kinetic parameters of an enzymatic reaction. 5. The compartmentation/solubility of an enzyme is another form of controlling the activity of an enzyme. Some enzymes exist as multienzyme or multifunctional complexes (Bisswanger and Schmincke-Ott, 1980; Perham, 2000; Reed, 1974; Srere, 1987). Some enzymes exist in isozymic forms: Within a single species, there may exist several different forms of enzyme catalyzing the same reaction; these are known as isozymes (Markert, 1975). Generally isozymes are derived from an association of different subunits in an oligomeric enzyme with different electrophoretic mobilities.

Enzymes are usually named with reference to the reaction they catalyze. It is customary to add the suffix -ase to the name of its major substrate. The Enzyme Commission (EC) has recommended nomenclature of enzymes based on the six major types of enzyme-catalyzed reactions (http://www.chem.qmw.ac.uk/iubmb/ enzyme/): EC EC EC EC EC EC

1: 2: 3: 4: 5: 6:

Oxidoreductases catalyze oxidation—reduction reactions. Transferases catalyze group transfer reactions. Hydrolases catalyze hydrolytic reactions. L yases catalyze cleavage and elimination reactions. Isomerases catalyze isomerization reactions. L igases catalyze synthetic reactions.

Thus, the EC numbers provide unique identifiers for enzyme functions and give us useful keyword entries in database searches. The ENZYME database at http://www.expasy.ch/enzyme/ provides information on EC number, name, catalytic activity, and hyperlinks to sequence data of enzymes. The 3D structures of enzymes can be accessed via Enzyme Structures Database at http://www.biochem.ucl.ac.uk/bsm/enzyme/index.html. Some other enzyme databases are listed in Table 7.1.

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TABLE 7.1. Enzyme Databases Web Site ENZYME DB: General information Enzyme structure database: Structures LIGAND: Enzyme reactions Brenda: General enzyme data EMP: General, literature summary Esther: Esterases Merops: Peptidases Protease CAZy: Carbohydrate active enzymes REBASE: Restriction enzymes Ribonuclease P database PKR: Protein kinase PlantsP: Plant protein kinases and phosphatase Aminoacyl-tRNA synthetases MDB: Metalloenzymes Promise: Prosthetic group/Metal enzymes Aldehyde dehydrogenase G6P dehydrogenase 2-Oxoacid dehydrogenase complex

URL http://www.expasy.ch/enzyme/ http://www.biochem.ucl.ac.uk/bsm/enzyme/index.html http://www.gebine.ad.jp/dbget/ligand.html http://www.brenda.uni-koeln.de/ http://wit.mcs.anl.gov/EMP/ http://www.ensam.inra.fr/cholinesterase/ http://www.bi.bbsrc.ac.uk/Merops/Merops.htm http://delphi.phys.univ-tours.fr/Prolysis http://afmb.cnrs-mrs.fr/:pedro/CAZY/db.html http://rebase.neh.com/rebase/rebase.html http://www.mbio.ncsu.edu/RnaseP/home.html http://pkr.sdsc.edu http://PlantP.sdsc.edu http://rose.man.poznan.pl/aars/index.html http://metallo.scripps.edu/ http://bmbsgi11.leads.ac.uk/promise/ http://www.ucshc.edu/alcdbase/aldhcov.html http://www.nal.usda.gov/fnic/foodcomp/ http://qcg.tran.wau.nl/local/pdhc.htm

7.2. KINETICS OF ENZYMATIC REACTIONS Enzyme kinetics (Ainsworth, 1977; Cornish-Bowden, 1995; Fromm, 1975; Plowman, 1972; Segel, 1975; Schulz, 1994), which investigates the rates of enzyme-catalyzed reactions as affected by various factors, offers an enormous potential to the study of enzyme reaction mechanisms and functions. Some important factors that affect the rates of enzymatic reactions are enzyme concentration, ligand (substrates, products, inhibitors, and activators) concentrations, solvent (solution, ionic strength, and pH), and temperature. When all these factors are properly analyzed, it is possible to learn a great deal about the nature of enzymes. The kinetic studies of an enzymatic reaction by varying ligand concentrations provide kinetic parameters that are essential for an understanding of the kinetic mechanism of the biochemical reaction. Operationally, the initial rate enzyme kinetics can be treated according to two assumptions:

7.2.1. Quasi-equilibrium Assumption Quasi-equilibrium, also known as rapid equilibrium, assumes that an enzyme (E) reacts with substrate (S) rapidly to form an enzyme—substrate complex (ES) (with a rate constant, k ) that breaks down to release the enzyme and product (P).  The enzyme, substrate, and the enzyme—substrate complex are at equilibrium; that is the rate at which ES dissociates to E ; S (rate constant of k ) is much faster than 

KINETICS OF ENZYMATIC REACTIONS

the rate of forming E ; P (rate constant of k ). Because enzyme kinetic studies are  carried out with excess concentrations of substrate — that is, [S]  [E] — the conservation equations [E] : [E] ; [ES] and [S] : [S] ; [ES] 5 [S] apply.    The overall rate of the reaction is limited by the breakdown of the enzyme—substrate complex, and the velocity is measured during the very early stage of the reaction. Because the quasi-equilibrium treatment expresses the enzyme—substrate complex in terms of [E], [S], and K — that is, [ES] : [E][S]/(K ; [S]) — the kinetic expressQ Q ion is obtained if we insert the expression for the enzyme—substrate complex into the rate expression: v : k [ES] : k [E][S]/(K ; [S]) : V [S]/(K ; [S])   Q Q This is known as the Michaelis—Menten equation, where there are two kinetic parameters, the maximum velocity V : k [E] and the Michaelis constant K (K ) :  Q K k /k .   The general rule for writing the rate equation according to the quasi-equilibrium treatment of enzyme kinetics can be exemplified for the random bisubstrate reaction with substrates A and B forming products P and Q (Figure 7.1), where K K : ? ?@ K K and K K : K K . @ @? N NO O ON 1. Write the initial velocity expression: v : k[EAB] 9 k
[EPQ], where the interconversion between the ternary complexes is associated with the rate constants k and k
in the forward and reverse directions, respectively. 2. Divide the velocity expression by the conservation equation for enzymes, [E] : [E] ; [EA] ; [EB] ; [EAB] ; [EPQ] ; [EP] ; [EQ], that is,  v/[E] :(k[EAB]9k
[EPQ])/([E];[EA];[EB];[EAB];[EPQ];[EP];[EQ])  3. Set the [E] term equal to unity, that is, [E] : 1. 4. The term for any enzyme-containing complex is composed of a numerator, which is the product of the concentrations of all ligands in the complex, and a denominator, which is the product of all dissociation constants between

Figure 7.1. Diagram for random bi bi kinetic mechanism. The random addition of substrates, A and B to form binary (EA and EB) and ternary (EAB) complexes. The two ternary complexes EAB and EPQ interconvert with the rate constant of k and k
. The release of products P and Q also proceeds in a random manner. Ks are dissociation constants where Ka Kab : Kb Kba and Kp Kpq : Kq Kqp .

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the complex and free enzyme, that is, [EA] : [A]/K , [EB] : [B]/K , ? @ [EP]:[P]/K , [EQ]:[Q]/K , [EAB]:([A][B])/(K K ), and [EPQ]: N O ? ?@ ([P][Q])/(K K ). O ON 5. The substitution yields the rate expression: k([A][B])/(K K )9k
([P][Q])/(K K )[E] ? ?@ O ON  v: 1;[A]/K ;[B]/K ;([A][B])/(K K );[P]/K ;[Q]/K ;([P][Q])/(K K ) ? @ ? ?@ N O O ON The rate expression for the forward direction is simplified to k([A][B])/(K K )[E] ? ?@  1 ; [A]/K ; [B]/K ; ([A][B])/(K K ) ? @ ? ?@ V [A][B] : K K ;K [A];K [B];[A][B] ? ?@ ?@ @?

v:

7.2.2. Steady-State Assumption The steady-state treatment of enzyme kinetics assumes that concentrations of the enzyme-containing intermediates remain constant during the period over which an initial velocity of the reaction is measured. Thus, the rates of changes in the concentrations of the enzyme-containing species equal zero. Under the same experimental conditions (i.e., [S]  [E] and the velocity is measured during the very   early stage of the reaction), the rate equation for one substrate reaction (uni uni reaction), if expressed in kinetic parameters (V and K ), has the form identical to the Q Michaelis—Menten equation. However, it is important to note the differences in the Michaelis constant that is, K : k /k for the quasi-equilibrium treatment whereas Q   K : (k ; k )/k for the steady-state treatment. Q    The general rule for writing the rate equation according to the steady-state treatment of enzyme kinetics by King and Altman method (King and Altman, 1956) can be illustrated for the sequential bisubstrate reaction. Figure 7.2 shows the ordered bi bi reaction with substrates A and B forming products P and Q. Each enzyme-containing species is associated with two rate constants, k in the forward  direction and k in the reverse direction.  The steady-state rate equation is obtained according to following rules (King and Altman method): 1. Write down all possible basic patterns with n 9 1 lines (n : number of enzyme forms that is, enzyme-containing species), in which all lines are connected without closed loops — for example,

2. The total line patterns equals m!(n 9 1)!(m 9 n ; 1)!, where m is the number of lines in the patterns.

KINETICS OF ENZYMATIC REACTIONS

Figure 7.2. Diagram for ordered bi bi kinetic mechanism. The free enzyme, E, binds to A (first substrate) to form a binary complex, EA, which then interacts with B (second substrate) to form a ternary complex, EAB. The two ternary complexes EAB and EPQ interconvert. The release of P (first product) forms EQ, which then dissociates to E and Q (second product) in an ordered sequence. k1 to k10 are rate constants.

3. Write a distribution equation for each enzyme form — for example, E/E :  N /D, where N and D are the numerator (for E) and denominator terms, C C respectively. 4. Numerator terms (e.g., N ) are written: C (a) Follow along the lines in the basic pattern in the direction from other enzyme forms (i.e., EA, EQ, EAB, and EPQ) leading toward the free enzyme form (i.e., E) for which the numerator is sought. (b) Multiply all the rate constants and concentration factors for this direction. (c) Repeat the process for all the basic patterns. (d) The numerator terms are the sum of all the products of rate constants and concentration factors. 5. Write the numerator terms for all the other enzyme forms by repeating the process — for example, N , N , N , and N for EA/E , EQ/E , EAB/E , C? CO C?@ CNO    and EPQ/E , respectively.  6. Denominator terms are the sum of all numerator terms, that is D : N ;N ;N ;N ;N . C C? CO C?@ CNO 7. Substitute appropriate distribution equations (e.g., EPQ/E and EQ/E ) into   the initial velocity expression: v : dP/dt : k [EPQ] 9 k [EQ][P]   : k EPQ/E [E] 9 k EQ/E [E] [P]       : (k k k k k [A][B]9k k k k k [P][Q])[E] )/k (k k ;k k ;k k )k                    ; k (k k ; k k ; k k )k [A] ; k k k k [B] ; k k k k [P]                 ; k k (k k ; k k ; k k ; k k )[A][B]           ; (k k ; k k ; k k ; k k )k k [P][Q]           ; k k k k [A][P] ; k k k k [B][Q]         ; k k k (k ; k )[A][B][P] ; k k k (k ; k )[B][P][Q]          

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This steady-state equation expressed with rate constants can be converted into the rate equation expressed with kinetic parameters according to Clelend (Cleland, 1963a, 1963b): v:

V V (AB9PQ/K )    (K K ;K A;K B;AB)V ;(K Q;K P;PQ)V /K ;(K BQ/K ;ABP/K )V ;(K AP/K ;BPQ/K )V /K G? @ @ ?  N O   ? GO GN  O G? G@  

where the equilibrium constant, K : (V K K )/(V K K ). V and V are maxi  N GO  @ G?   mum velocities for the forward and reverse reactions. K , K , K , and K are ? @ N O Michaelis constants, while K , K , K , and K are inhibition constants associated G? G@ GN GO with substrates (A and B) and products (P and Q), respectively. The rate equation for the forward reaction can be simplified (Table 7.2) to v:

V AB  K K ; K A ; K B ; AB G? @ @ ?

7.2.3. Cleland’s Approach The Cleland nomenclature (Cleland, 1963a) for enzyme reactions follows: 1. The number of kinetically important substrates or products is designated by the syllables Uni, Bi, Ter, Quad, Pent, and so on, as they appear in the mechanism. TABLE 7.2. Cleland Nomenclature for Bisubstrate Reactions Exemplifieda Mechanism

Cleland Representation

Forward Rate Equation

Order bi bi

v:

V AB  K K ; K A ; K B ; AB G? @ @ ?

Random bi bi

v:

V AB  K K ; K A ; K B ; AB G? @ @ ?

Ping pong bi bi or Uni uni uni uni ping pong

v:

V AB  K A ; K B ; AB @ ?

?Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi bi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1/v versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (K K ) in the denominator. These three kinetic mechanisms can be further G? @ differentiated by their product inhibition patterns (Cleland, 1963b). Note: V , K , K , and K are maximum velocity, Michaelis constants for A and B, and inhibition constant  ? @ G? for A, respectively.

KINETICS OF ENZYMATIC REACTIONS

2. A sequential mechanism will be one in which all the substrates must be present on the enzyme before any product can leave. Sequential mechanisms will be designated ordered or random depending on whether the substrate adds and the product releases in an obligatory sequence or in a nonobligatory sequence. 3. A ping pong mechanism will be designated if one or more products are released during the substrate addition sequence, thereby breaking the substrate addition sequence into two or more segments. Each segment is given an appropriate syllable corresponding to the number of substrate additions and product releases. 4. The letters A, B, C, D designate substrate in the order of their addition to the enzyme. Products are P, Q, R, S in the order of their release. Stable enzyme forms are designated by E, F, G, H, with E being free enzyme. 5. Isomerization of a stable enzyme form as a part of the reaction sequence is designated by the prefix Iso, such as Iso ordered, Iso ping pong. 6. For expressing enzymatic reactions, the sequence is written from left to right with a horizontal line or group of lines representing the enzyme in its various forms. Substrate additions and product releases are indicated by the downward ( ) and upward (!) vertical arrows, respectively. 7. Each arrow is associated with the corresponding reversible step — that is, one rate constant each with the forward and reverse directions. Generally, odd-numbered rate constants are used for the forward reactions whereas even-numbered ones are used for the reverse direction. Examples of the bisubstrate reactions according to Cleland nomenclature are listed in Table 7.2. For multisubstrate enzymatic reactions, the rate equation can be expressed with respect to each substrate as an n:m function, where n and m are the highest order of the substrate for the numerator and denominator terms respectively (Bardsley and Childs, 1975). Thus the forward rate equation for the random bi bi derived according to the quasi-equilibrium assumption is a 1:1 function in both A and B (i.e., first order in both A and B). However, the rate equation for the random bi bi based on the steady-state assumption yields a 2:2 function (i.e., second order in both A and B). The 2:2 function rate equation results in nonlinear kinetics that should be differentiated from other nonlinear kinetics such as allosteric/cooperative kinetics (Chapter 6, Bardsley and Waight, 1978) and formation of the abortive substrate complex (Dalziel and Dickinson, 1966; Tsai, 1978).

7.2.4. Environmental Effects The rate of an enzymatic reaction is affected by a number of environmental factors, such as solvent, ionic strength, temperature, pH, and presence of inhibitor/activator. Some of these effects are described below. Presence of Inhibitors: inhibition Kinetics. The kinetic study of an enzymatic reaction in the presence of inhibitors is one of the most important diagnostic procedures for enzymologists. The inhibition (reduction in the rate) of an enzyme

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TABLE 7.3. Types of Enzyme Inhibitions Type of Inhibition

Complex Formation

Control

E ; S : ES ; E ; P

Competitive

E ; I : EI

Uncompetitive

ES ; I : ESI

Noncompetitive or mixed competitive

E ; I : EI

)GQ

)GG

)GQ

)GG

Forward Rate Equation v:

V S  K ;S Q

V S  K (1 ; I/K ) ; S Q GQ V S  v: K s ; S(1 ; I/K ) ? GG V S  v: K (1;I/K );S(1;I/K ) Q GQ GG v:

ES ; I : ESI Note: K and K are inhibition (dissociation) constants for the formation of the inhibitor complexes in GG GQ which the subscripts denote the intercept effect and slope effect, respectively.

reaction is one of the major regulatory devices of living cells and offers great potentials for the development of pharmaceuticals. An irreversible inhibitor forms the stable enzyme complex or modifies the enzyme to abolish its activity, whereas a reversible inhibitor (I) forms dynamic complex(es) with the enzyme (E) or the enzyme substrate complex (ES) by reducing the rate of the enzymatic reaction (see Table 7.3). Temperature Effect: Determination of Activation Energy. From the transition state theory of chemical reactions, an expression for the variation of the rate constant, k, with temperature known as the Arrhenius equation can be written k : Ae\#?02 or ln k : ln A 9 E /RT ? where A, R, and T are preexponential factor (collision frequency), gas constant, and absolute temperature, respectively. E is the activation energy that is related to the ? enthalpy of formation of the transition state complex, H ‡, of the reaction E : H ‡ ; RT. The lowering of the activation energy of an enzymatic reaction is ? achieved by the introduction into the reaction pathway of a number of reaction intermediate(s). pH Effect: Estimation of pKa Value(s). Some of the possible effects that are caused by a change in pH are: 1. Change in the ionization of groups involved in catalysis 2. Change in the ionization of groups involved in binding the substrate

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3. Change in the ionization of substrate(s) 4. Change in the ionization of other groups in the enzyme 5. Denaturation of the enzyme The pH effect on kinetic parameters (pH-rate/binding profile) may provide useful information on the ionizaing groups of the enzyme if the kinetic studies are carried out with nonionizable substrate in the pH region (pH 5—9) where enzyme denaturation is minimum. If the Michaelis constant (K) and/or the maximum velocity (V ) vary with pH, the number and pK values of the ionizing group(s) can be inferred from the shape of pH-rate profile (pH versus pK and pH versus log V plots), namely, full bell shape for two ionizing groups and half bell shape for one ionizing group (see Table 7.4). The initial rate enzyme kinetics uses very low enzyme concentrations (e.g., 0.1 M to 0.1 pM) to investigate the steady-state region of enzyme-catalyzed reactions. To investigate an enzymatic reaction before the steady state (i.e., transient state), special techniques known as transient kinetics (Eigen and Hammes, 1963) are employed. The student should consult chapters of kinetic texts (Hammes, 1982; Robert, 1977) on the topics. KinTekSim (http://www.kintek-corp.com/kinteksim.htm) is the Windows version of KINSIM/FITSIM (Frieden, 1993) which analyzes and simulate enzyme-catalyzed reactions.

7.3. SEARCH AND ANALYSIS OF ENZYME DATA 7.3.1. Search for Enzyme Database The ENZYME nomenclature database (Figure 7.3) of ExPASy (Expert Protein Analysis System) at http://www.expasy.ch/enzyme/ can be searched by entering EC number or enzyme names. The query returns information on EC number, enzyme name, catalytic activity, cofactors (if any) and pointers to Swiss-Prot sequence, ProSite, and human disease(s) of the enzyme deficiency. LIGAND (Goto et al., 2002) at http://www.gebine.ad.jp/dbget/ligand.html is a composite database comprising

TABLE 7.4. pH Effects on Enzyme Kinetics Diagnostic pH-Rate Profile Full bell Left half bell Right half bell Full bell Left half bell Right half bell Note: K



Rate Expression

Low pH

High pH

K:K /(H/K ;1;K /H) K   K:K /(H/K ;1) K  K:K /(1;K /H) K  V :V /(H/K ;1;K /H) K   V :V /(H/K ;1) K  V :V /(1;K /H) K 

log K:log K 9pK ;pH K  log K:log K 9pK ;pH K 

log K:log K ;pK 9pH K 

log V :log V 9pK ;pH K  log V :log V 9pK ;pH K 

log K:log K ;pK 9pH K  log V :log V ;pK 9pH K  log V :log V ;pK 9pH K 

and K or K and K are ionizing group(s) in the free enzyme or the enzyme—substrate complex, respectively.   

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Figure 7.3. Enzyme nomenclature database of ExPASy.

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Enzyme for the information on enzyme molecules and enzymatic reactions Compound for the information on metabolites Reaction for the collection of substrate—product relationships

Select Search enzymes and compounds under DBGet/LinkDB Search to open query page (Figure 7.4). Enter the enzyme name or the substrate name in the bfind mode and click the Submit button. From the list of hits, select the desired entry by clicking the EC name. This returns information on name, class, reaction, pointers to structures of substrates/products/cofactor, links to pathway for which the selected enzyme is the member enzyme of the pathway, and related databases. BRENDA (Schomburg et al., 2002) is the comprehensive enzyme information system that can be accessed at http://www.brenda.unikoeln.de/. Select New Query Forms to initiate Search by EC number, by Enzyme name or by Organism (Figure 7.5). Enter the EC number or the enzyme name (you can use * for partial name, e.g., *kinase) and click Query. From the list of hits (only one entry is returned with EC number), select the desired entry by clicking the EC number. The request returns the following information (the available information differs with each enzyme, e.g., for lysozyme): EC number, Organism, Systematic name, Recommended name, Synonyms, CAS registry number, Reaction, Reaction type, Substrates/products, Natural substrate, Turnover number [1/min], Specific activity [mol/min/mg], K value K [mM], pH optimum, pH range, Temperature optimum [°C], Temperature range [°C], Cofactors, Prosthetic groups, Activating substances, Metal/ions, Inhibitors, Source/tissue, Localization, Purification, Crystallization, Molecular weight, Subunits,

SEARCH AND ANALYSIS OF ENZYME DATA

Figure 7.4. LIGAND database. A composite database for searching/retrieving enzyme information by enzyme name, EC number, substrates/products, and reactions.

Figure 7.5. Search enzyme information at Brenda. Brenda is the comprehensive enzyme database for retrieving chemical, kinetic, and structural properties of enzymes via EC number, enzyme name, and organism (biological source). The search page by EC number is shown.

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Figure 7.6. Enzymology database, EMP. The enzyme data published in literatures can be searched/retrieved from EMP via enzyme name/EC code and biological sources.

Cloned, pH stability, Temperature stability [°C], Organic solvent stability, Oxidation stability, General stability, Storage stability, Renatured, and Links to other databases and references. EMP at http://wit.mcs.anl.gov/EMP/ is the resource site for summarized enzyme data that have been published in the literature. The site opens with the Simple query form (Figure 7.6). Enter the enzyme name into the name query box of ‘Find an enzyme,’ select ‘Common name,’ then enter the common organism name for ‘In an organism or taxon,’ and enter tissue name in response to ‘Extracted from.’ Clicking Submit Query returns an itemized summary of published enzyme data (data from one article may appear in more than one entries for different substrates) including concise assay and purification procedures, kinetic equations and kinetic parameters. The Enzyme Structure Database (http://www.biochem.ucl.ac.uk/bsm/enzymes/ index.html), which contains the known enzyme structures of PDB, can be searched via EC number hierarchically (Figure 7.7). The search returns a list of individual pdb files with a link to CATH and pointers to PDBsum, ExPaSy, KEGG, and WIT. Clicking PDBsum opens the PDBsum page, which contains descriptive headings of enzyme, CATH classification, amino acid sequence with secondary structure designation, clickable PROMOTIF summary, TOPS (protein topology cartoon of related representative enzyme), PROSITE patterns, MolScript picture, as well as graphical presentations of ligand/ligand—active-site interactions. Click LIGPLOT of interactions (under Ligand) to display ligand—active site interactions (Figure 7.8). Pressing the RasMol button changes the view window into the RasMol window (if RasMol

Figure 7.7. Home page of enzyme structure database. Links to enzyme structure and analysis servers are available at the Enzyme Structure Database which extracts and collects enzyme structures from pdb files.

Figure 7.8. The substrate interaction at the active site of an enzyme. The interaction of tetra-N,N,N,N-acetylchitotetraose (NAG4) with amino acid residues at the active site of lysozyme (1LZC.pdb) can be viewed/saved at PDBsum server (Enyme Structure Database;PDBsum;LIGPLOT of interactions under Ligand) linked to the Enzyme Structure Database.

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is installed). Right click on the window to open the menu box (File, Edit, Display, Color, Options, and Rotation). The coordinate file of the ligand—active-site interaction can be saved (PDB format or MDL mol format) by selecting File;Save Molecule As. The PDBsum can be accessed directly at http:// www.biochem.ucl.ac.uk/bsm/pdbsum/. 7.3.2. Analysis of Kinetic Data For the statistical and computer analysis of enzyme kinetic data, the students should consult published articles on the topics (Cleland, 1967; Crabble, 1992; Wilkinson, 1961). The software DynaFit, applicable to enzyme kinetic analysis, has been described (Chapter 6). In this chapter the program Leonora, which accompanies the text Analysis of Enzyme Kinetic Data by A. Cornish-Bowden (Cornish-Bowden, 1995), will be used to perform regression analysis of enzyme kinetic data. The software can be downloaded from http://ir2lcb.cnrs-mrs.fr/¨athel/leonora0.htm. After installation, launch the program (MS-DOS) to open the Main menu providing a list executable commands (Figure 7.9). Type D (select Data) to bring the Data menu, and type I (select Input new data) to enter kinetic data. Use Tab key to move across the columns and arrow keys to move up and down the rows. Enter label on the row 1 and data for the others. Press Esc to complete the data entry. Furnish short description for the Title, type N to enter filename, and save the data file (.mmd). Type X to exit the Data menu and return to the Main menu. Type Q (Equation) to select the appropriate rate equation from the pop-up Model menu (the list differs depending on kinetic data file). The menu entries of the equations are listed in Table 7.5. To save the kinetic results, key in O for Output requirement and then R for Result page (Figure 7.10), which lists fitted kinetic parameters. Exit to the Calculations menu by typing C. Define method and weighting system, then C to calculate

Figure 7.9. Starting page of Leonora.

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SEARCH AND ANALYSIS OF ENZYME DATA

TABLE 7.5. Representative Menu Entries of Kinetic Equations in Leonora Equations by Name

Algebraical Equations

Michaelis—Menten Substrate inhibition Michaelis-Menten (ignoring [I]) Primary Michaelis—Menten (at each [I]) Generic inhibition, (at each [S]) Competitive inhibition Uncompetitive inhibition Mixed inhibition Michaelis—Menten (ignoring [B]) Michaelis—Menten (ignoring [A]) Primary Michaelis—Menten (at each [B]) Primary Michaelis—Menten (at each [A]) Substituted enzyme mechanism Ternary-complex mechanism Ordered equilibrium mechanism S-shaped pH profile Z-shaped pH profile Bell-shaped pH profile

M: S: M: P: G: C: U: I: M: I: P: R: S: T: O: S: Z: B:

v : V [S]/(K ; [S]) K v : V [S]/(K ; [S](1 ; [S]/K )) K QG v : V [S]/(K ; [S]) K v : V [S]/(K ; [S])  K  v : v/(1 ; [I]/K ) G v : V [S]/(K (1 ; [I]/K ) ; [S]) K GA v : V [S]/(K ; [S](1 ; [I]/K )) K GS v : V [S]/(K (1 ; [I]/K ) ; [S](1 ; [I]/K )) K GA GS v : V [A]/(K ; [A]) K v : V [B]/(K ; [B]) K v : V [A]/(K ; [A])  K  v : V [A]/(K ; [A])  K  v : V [A][B]/(K [A] ; K [B] ; [A][B]) K K v : V [A][B]/(K ; K [A] ; K [B] ; [A][B])  K K v : V [A][B]/(K ; K [A] ; [A][B])  K k : K /(1 ; [H>]/K )  k : K /(1 ; K /[H>])  k : K /(1 ; [H>]/K ; K /[H>])  

Notes: Reprinted from table 9.1 (p. 156) from Analysis of Enzyme Kinetic Data by Athel Cornish-Bowden (1995) by permission of Oxford University Press. 1. The default Michaelis—Menten refers to uni uni or uni bi rate equation. 2. Mixed inhibition and noncompetitive inhibition can be used interchangeably. 3. Substituted-enzyme mechanism refers to ping pong bi bi mechanism. 4. Ternary-complex mechanism refers to order bi bi mechanism. 5. Michaelis—Menten, ignoring [X] refers to kinetic treatment of the bi bi reaction, A;B by ignoring the X (either A or B). 6. S-Shaped, Z-shaped and bell-shaped pH profiles refer to right-half, left-half and full bell profiles respectively.

best fit. To view the graphical results, type P for Plot results (which becomes active after calculations). Define Axes and Scale ranges. Use Tab key to move between abscissa and ordinate, and use arrow keys to define plotting parameters (e.g., 1/v). Type P to Plot.

Figure 7.10. Result page of Leonora.

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DYNAMIC BIOCHEMISTRY: ENZYME KINETICS

7.4. WORKSHOPS 1. The active-site-directed inhibition of enzymes has been an important research topic in pharmaceutical drug design (Sandler, 1980). An early development of anti-cancer agents involved inhibitions of dihydrofolate reductase and thymidylate synthetase. Search enzyme resource sites for kinetic data (turnover number, K and K K ) of these two enzymes. G 2. Enzymes are highly selective of the substrates with which they interact and in the reactions that they catalyze. This selective nature of enzymes collectively known as enzyme specificity can be best illustrated with oxidoreductases (dehydrogenases), which display substrate and bond specificities (e.g., acting on sCHOHs, versus sCHO versus sCHsCHs versus sCHNH , and cis versus  trans for unsaturated substrates), coenzyme specificity (e.g., NAD(H) versus NADP(H)), chiral stereospecificity (- versus - or R- versus S-stereoisomers), and prochiral stereospecificity (A versus B corresponding to proR- versus proS isomers and re face versus si face, respectively). The table lists some dehydrogenases and their coenzyme, substrate, product and stereospecificities (You, 1982): Oxidoreductase Alcohol DH Alcohol DH Alcohol DH(Aldehyde, RD) Alcohol DH(Aldehyde, RD) Homoserine DH Glycerol DH Glycerol DH Glycerol-3P DH Glycerol-3P DH XylitolDH (Xylu RD) Xylitol DH(Xylu RD) Mannitol-1P DH Polyol DH (Aldose RD) UDPGlucose DH Shikimate DH -Lactate DH -Lactate DH Glycerate DH 3-Hydroxybutyrate DH Malate DH Malate DH (decarboxyl) Isocitrate DH Isocitrate DH P-Gluconate DH Glucose DH Galactose DH Glucose-6P DH Glucose-6P DH Aryl alcohol DH P-Glycerate DH Carnitine DH

Source

Substrate

Product

Coenzy

Stereo

Horse liver Yeast Fruit fly

Ethanol Ethanol Glycerol

Acetaldehyde Acetaldehyde -Glyceraldehyde

NAD NAD NADP

A A A

Human liver

Glycerol

-Glyceraldehyde

NADP

A

Pea Aerobacter aerogenes Rabbit muscle E. coli Rabbit muscle Yeast Pigeon liver E. coli Human placenta

-Homoserine Glycerol Glycerol SnGlycerol-3P SnGlycerol-3P Xylitol Xylitol -Mannitol-1P -Sorbitol

-Adpsemiald DiOHacetone -Glyceraldehyde DiOHacetone P DiOHacetone P -Xylulose -Xylulose -Fructose-6P -Glucose

NADP NAD NADP NADP NAD NAD NADP NAD NADP

B A A B B B B B A

Beef liver Pea L actobacillus arabinosus L actobacillus arabinosus Spinach Beef heart

UDPGlucose Shikimate -Lactate

UDPGlucuronate 5-DeHshikimate Pyruvate

NAD NADP NAD

B A A

-Lactate

Pyruvate

NAD

A

-Glycerate -OHbutyrate

Hydroxyacetone Acetoacetate

NAD NAD

A B

Pig heart Pigeon liver

-Malate -Malate

Oxaloacetate Pyruvate

NAD NADP

A A

Pea Pea Yeast Beef liver Pseud. fluorescens L . mesenteroides Yeast Rabbit kid cortex E. coli Pseud. aeruginosa

threo-Isocitrate threo-Isocitrate 6P--Gluconate --Glucose --Galactose -Glucose-6P -Glucose-6P Benzyl alcohol P-OHPyruvate Carnitine

-Ketoglutarate -Ketoglutarate -Ribulose-5P Gluc--lactone Gal- -lactone Glu-lactone6P Glu-lactone6P Benzaldehyde Glycerate-3P 3-DeHCarnitine

NAD NADP NADP NAD NAD NAD NADP NADP NAD NAD

A A B B B B B B A B

Oxidoreductase -Fucose DH Sorbose DH Aldehyde DH Acetaldehyde DH (acyl) Asp-semialdehyde DH Glyceraldehyde-P DH Glyceraldehyde-P DH Succinate semiald DH Inosine monoP DH Xanthine DH Cortisone -RD Cortisone -RD Cortisone -RD Cortisone -RD Meso-Tartrate DH Acyl CoA DH Alanine DH Glutamate DH Glutamate DH Dihydrofolate RD Glutathione RD Lipoamide DH Nitrate RD Nitrite RD Hydroxylamine RD

Source Sheep liver Yeast Yeast Clost. kluyveri E. coli Rabbit muscle Pea Psudomonas Aerob. aerogenes Chicken liver Rat liver, soluble Rat liver, micros Rat liver, soluble Rat liver, micros Pseud. putida Rat liver, mictochondria Bacillus subtilis Pea mitochondria Yeast Chicken liver Yeast Pig heart Spinach Yeast Yeast

Substrate -Fucose -Sorbose Acetaldehyde Acetaldehyde -Asp-semaldehyde -Glycerald-3P -Glycerald-3P Succ semialdehyde 5
-IMP Xanthine Testosterone Progesterone Testosterone Progesterone meso-Tartrate Octanoyl CoA -Alanine -Glutamate -Glutamate Tetrahydrofolate ox Glutathione DiHlipoamide NO\  NO\  NH OH 

Product

Coenzy

Stereo

-Fuc--lactone 5Keto-fructose Acetate Acetyl CoA --Asp-P -3-P Glycerate 1,3-diPGlycerate Succinate 5
-XMP Urate 5Htestosterone 5Pregnandione 5Htestosterone 5Pregnandione DiOH Fumarate Oct-2-enoyl CoA Pyruvate -Ketoglutarate -Ketoglutarate Dihydrofolate red Glutathione (;)-Lipoamide NO\  NH OH NH 

NAD NADP NAD NAD NADP NAD NAD NAD NAD NAD NADPH NADPH NADPH NADPH NAD NADP NAD NAD NADP NADP NADPH NAD NADH NADPH NADPH

B A A A B B B A B B A A B B A A A B B A B B A B B

Note: Abbreviations used are: DH, dehydrogenase; RD, reductase; coenzy, coenzyme; stereo, stereospecificity; ox, oxidized; red, reduced; H, hydro-; OH, hydroxy-; and P, phospho-/phosphate. Source: Partially reproduced with the permission from Academic Press.

Apply Microsoft Access to design a database appended with queries for retrieving groups of dehydrogenases according to their coenzyme specificity and stereospecificity. 3. Search enzyme databases for information to construct a database of glucosidases (EC 3.2.1.x) with retrievable fields on substrate (anomeric) specificity, catalytic mechanism (stereochemical, e.g., inversion versus retention) and kinetic constants (e.g., K and V ). K 4. The catalytic residues of serine proteases such as chymotrypsin generally involve catalytic triad of Asp, His, and Ser residues, for example,

Search the Enzyme Structure Database for -chymotrypsin active site (by the aid of the active-site-modified enzyme or active-site-specific inhibitor—enzyme complex) to identify and depict (save pdb file) the catalytic triad of -chymotrypsin. 5. Initial rates of a hydrolase (10.0 nM)-catalyzed reaction are measured and tabulated overleaf. Evaluate the kinetic parameters of this Uni-substrate reaction. Calculate the turnover number of the enzyme.

142

DYNAMIC BIOCHEMISTRY: ENZYME KINETICS

Substrate (mM)

Rates (M/min)

1.00 ; 10\ 2.00 ; 10\ 5.00 ; 10\ 1.00 ; 10\ 2.00 ; 10\ 5.00 ; 10\

0.179 0.305 0.534 0.718 0.870 0.981

6. Initial rates of an esterase-catalyzed reactions in the absence and presence of 0.10 mM each of inhibitors I and J are measured and tabulated below. Evaluate the kinetic and inhibition parameters of this Uni-substrate reaction. Rates (M/min) I (mM)

J (mM)

Ester (mM)

No Inhibitor

0.10

0.25

0.10

0.25

1.00 ; 10\ 2.00 ; 10\ 5.00 ; 10\ 1.00 ; 10\ 2.00 ; 10\ 5.00 ; 10\

0.114 0.190 0.321 0.414 0.485 0.542

0.099 0.169 0.291 0.385 0.465 0.526

0.072 0.128 0.238 0.340 0.424 0.483

0.097 0.163 0.272 0.361 0.417 0.467

0.084 0.141 0.239 0.309 0.362 0.392

7. The steady-state kinetic studies of liver alcohol dehydrogenase (12.5 nM) are performed. The initial rates (v in M/min) with varying substrate concentrations in both directions (forward for ethanol oxidation and reverse for ethanal reduction) are given below. Evaluate their kinetic parameters and equilibrium constant. NAD> (mM) Ethanal (mM) 0.50 1.0 2.0 5.0 10 NADH (mM) Ethanal (mM) 0.50 1.0 2.0 5.0

 

0.10

0.20

0.50

0.80

0.16 0.24 0.31 0.38 0.45

0.19 0.28 0.37 0.45 0.52

0.22 0.30 0.42 0.52 0.63

0.26 0.34 0.49 0.60 0.72

0.010

0.020

0.040

0.050

0.042 0.050 0.054 0.063

0.049 0.059 0.063 0.074

0.056 0.067 0.073 0.086

0.062 0.074 0.084 0.098

143

WORKSHOPS

8. The initial rates (v in M/min) of liver alcohol dehydrogenase-catalyzed ethanal reduction are measured in the presence of pyrazole as an inhibitor at the constant concentration of NADH (0.02 M) and the constant concentration of ethanal (2.0 mM), respectively. Propose respective inhibition types and estimate their inhibition constants. Ethanal (mM) Pyrazole (M) 0 1.0 2.0 5.0 NADH (mM) Pyrazole (M) 0 1.0 2.0 5.0

 

0.50

1.0

2.0

5.0

0.034 0.027 0.022 0.008

0.040 0.030 0.024 0.010

0.044 0.033 0.026 0.011

0.050 0.036 0.028 0.013

0.010

0.020

0.050

0.10

0.032 0.022 0.016 0.006

0.040 0.024 0.018 0.008

0.046 0.027 0.020 0.010

0.052 0.030 0.022 0.011

9. Kinetic studies of an esterase catalysis are carried out at various pH values and initial rates (v in M/sec) of hydrolysis are tabulated below: Ester (mM) pH 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5



0.01

0.02

8.04;10\ 1.29;10\ 2.95;10\ 4.40;10\ 0.105 0.158 0.227 0.342 0.296 0.455 0.256 0.481 0.190 0.282 9.62;10\ 0.144 3.02;10\ 4.53;10\

0.05

0.10

0.20

1.84;10\ 6.13;10\ 0.225 0.498 0.625 0.690 0.412 0.205 6.46;10\

2.36;10\ 7.27;10\ 0.263 0.559 0.735 0.794 0.485 0.238 7.54;10\

2.48;10\ 7.91;10\ 0.279 0.625 0.826 0.847 0.505 0.256 8.14;10\

Perform data analysis and evaluate pK value(s) of ionizing group(s). 10. Quantitative structure—activity relationship (QSAR) (Hansch and Klein, 1986; Hansch and Leo, 1995) represents an attempt to correlate structural descriptors of compounds with activities. The physicochemical descriptors include numerical parameters to account for electronic properties, steric effect, topology, and hydrophobicity of analogous compounds. In its simplest form, the biochemical activities are correlated to the numerical substituent descriptors of analogous compounds tested by a linear equation such as log k (or K or 1/C) :  ; E ; ; d Q

144

DYNAMIC BIOCHEMISTRY: ENZYME KINETICS

where k, K, and C are rate constant, binding constant, and molar concentration producing a standard biological response in a constant time interval by the compound.  ( for aromatic compounds and * for aliphatic compounds), E , and Q are the most widely used descriptors for electronic property, steric hindrance, and hydrophobicity associated with the substituent of congeners under investigation. The correlation equation is solved by the regression analysis to yield correlation coefficients for the electronic ( ), steric (), and hydrophobic ( ) effects of the compounds on the measured biochemical activities. Kinetic studies of -chymotrypsin catalyzed hydrolysis of p-nitrophenyl esters are carried out (Duprix et al., 1970): O

RsOsOs

O

sNO2 ; H2O _ RsCsOH ; HOs

sNO2

The rate constants for deacylation step (k ) and common descriptors associated with B? substituents (R) are summarized below: Substituent, R H CH  (CH ) CH  (CH ) C  CH OCH   ICH  ClCH  Cl(CH )  Cl(CH )  Cl(CH )  C H CH    C H (CH )    C H (CH )    C H (CH )   



E Q



log k 

0.49 0.00 90.19 90.30 0.64 0.85 1.05 0.38 0.14 0.05 0.21 0.08 0.02 0.02

1.10 0.00 90.47 91.54 90.19 90.37 90.24 90.90 90.40 90.40 90.38 90.38 90.45 90.45

0.00 0.50 1.30 1.68 0.03 1.50 0.89 1.39 1.89 2.39 2.63 3.13 3.63 4.13

0.18 92.00 92.47 93.74 90.47 90.24 90.42 91.68 91.29 91.35 91.73 90.75 90.92 91.73

Perform the regression analyses for the descriptors to assess the contribution of substituent effect(s) on the rate of -chymotrypsin-catalyzed hydrolysis of p-nitrophenyl esters. Referring to the catalytic triad of chymotrypsin, rationalize your results for the plausible reaction mechanism.

REFERENCES Ainsworth, S. (1977) Steady-State Enzyme Kinetics. University Park Press. Baltimore, MD. Bardsley, W. G., and Childs, R. E. (1975) Biochem. J. 149:313—328. Bardsley, W. G., and Waight, R. D. (1978) J. T heor. Biol. 70:135—156. Benkovic, S. J. (1992) Annu. Rev. Biochem. 61:29—54. Bisswanger, H., and Schmincke-Ott, E., Eds. (1980) Multifunctional Proteins. John Wiley & Sons, New York.

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Schulz, A. R. (1994) Enzyme Kinetics. Cambridge University Press, Cambridge. Scott, W. G., and Klug, A. (1996) Trends Biochem. Sci. 21:220—224. Segel, I. H. (1975) Enzyme Kinetics. Wiley—Interscience. New York. Sheppard, T. L., Ordoukhanian, P., and Joyce, G. F. (2000) Proc. Natl. Acad. Sci. U.S.A. 97:7802—7807. Srere, P. A. (1987) Annu. Rev. Biochem. 56:89—124. Tsai, C. S. (1978) Biochem. J. 173:483—496. Wilkinson, G. N. (1961) Biochem. J. 80:324—332. You, K. (1982) Meth. Enzymol. 87:101—126.